Subgroups — #26033926

Order 11392.

1522 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152258	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152257	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152249	C₂	1	2	yes	maximal, complemented
8	#19152247	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152246	C₂	1	2	yes	maximal, complemented
10	#19152243	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152240	C₂	1	2	yes	maximal, complemented
12	#19152237	C₂	1	2	yes	maximal, complemented
13	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152178	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152175	C₂	1	2	yes	maximal, complemented
16	#19152173	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152170	C₂	1	2	yes	maximal, complemented
18	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152106	C₂	1	2	yes	maximal, complemented
20	C₂×#15667990	C₂	1	2	yes	maximal, complemented
21	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152077	C₂	1	1	yes	maximal, characteristic, complemented
23	#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#15668059	—	2	8	no	—
25	C₂×#13083575	C₂²	1	1	yes	characteristic
26	C₂×#13083574	C₂²	1	2	yes	—
27	C₂×#13083574	C₂²	1	1	yes	characteristic
28	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13083574	C₂²	1	2	yes	complemented
30	C₂×#13083573	C₂²	1	2	yes	—
31	C₂×#13083573	C₂²	1	1	yes	characteristic
32	C₂×#13083573	C₂²	1	2	yes	complemented
33	C₂×#13083573	C₂²	1	2	yes	complemented
34	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
35	#41×D₈₉	—	2	8	no	—
36	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
37	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
39	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
42	C₂×D₄×D₈₉	C₂²	1	2	yes	—
43	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄×D₈₉	C₂²	1	2	yes	—
45	#15668011	C₂²	1	2	yes	complemented
46	#15668011	C₂²	1	2	yes	complemented
47	#15668010	C₂²	1	1	yes	characteristic, complemented
48	#15668001	C₂²	1	1	yes	characteristic, complemented
49	#15668000	C₂²	1	1	yes	characteristic, complemented
50	#15667998	C₂²	1	2	yes	complemented
51	#15667998	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667997	C₂²	1	2	yes	complemented
54	#15667997	C₂²	1	1	yes	characteristic, complemented
55	#15667996	C₂²	1	2	yes	complemented
56	#15667995	C₂²	1	2	yes	complemented
57	#15667995	C₂²	1	2	yes	complemented
58	#15667994	C₂²	1	1	yes	characteristic, complemented
59	#15667993	C₂²	1	2	yes	complemented
60	#15667992	C₂²	1	1	yes	characteristic
61	#15667991	C₂²	1	1	yes	characteristic, complemented
62	#15667990	C₂²	1	2	yes	—
63	#15667990	C₂²	1	2	yes	—
64	#15667990	C₂²	1	2	yes	—
65	#15667990	C₂²	1	1	yes	characteristic
66	#15667990	C₂²	1	2	yes	complemented
67	#15667990	C₂²	1	2	yes	complemented
68	#15667990	C₂²	1	2	yes	complemented
69	#15667990	C₂²	1	2	yes	complemented
70	#15667990	C₂²	1	2	yes	complemented
71	#15667990	C₂²	1	2	yes	complemented
72	#15667989	C₂²	1	1	yes	characteristic, complemented
73	#15667989	C₂²	1	2	yes	complemented
74	#15667989	C₂²	1	2	yes	complemented
75	#15667988	C₂²	1	1	yes	characteristic
76	#15667988	C₂²	1	1	yes	characteristic, complemented
77	#15667987	C₂²	1	2	yes	complemented
78	#15667987	C₂²	1	1	yes	characteristic, complemented
79	#15667986	C₂²	1	2	yes	complemented
80	#15667986	C₂²	1	1	yes	characteristic, complemented
81	#15667985	C₂²	1	1	yes	characteristic
82	#15667985	C₂²	1	2	yes	complemented
83	#15667985	C₂²	1	2	yes	complemented
84	#15667985	C₂²	1	2	yes	complemented
85	#15667984	C₂²	1	1	yes	characteristic, complemented
86	#15667984	C₂²	1	2	yes	complemented
87	#15667984	C₂²	1	2	yes	complemented
88	#15667984	C₂²	1	2	yes	complemented
89	#15667982	C₂²	1	1	yes	characteristic
90	#15667982	C₂²	1	2	yes	—
91	#15667980	C₂²	1	2	yes	—
92	#15667980	C₂²	1	1	yes	characteristic
93	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
94	#15667977	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
96	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
97	#15667974	C₂²	1	2	yes	—
98	#15667974	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
102	#15667972	C₂²	1	2	yes	—
103	#15667972	C₂²	1	2	yes	complemented
104	#15667972	C₂²	1	2	yes	complemented
105	#15667969	C₂²	1	1	yes	characteristic, complemented
106	#15667968	C₂²	1	2	yes	complemented
107	C₂×#13083553	C₂²	1	2	yes	complemented
108	C₂×#13083553	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂×#13083551	C₂²	1	2	yes	—
112	C₂×#13083551	C₂²	1	2	yes	—
113	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
114	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
115	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#123×C₈₉	C₂²	1	2	yes	complemented
118	#123×C₈₉	C₂²	1	2	yes	complemented
119	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#121×C₈₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
125	C₂³×D₈₉	C₂³	1	1	yes	characteristic
126	C₂³×D₈₉	C₂³	1	2	yes	—
127	#13083575	—	2	4	no	—
128	#13083574	—	2	8	no	—
129	#13083574	—	2	8	no	—
130	#13083574	—	2	4	no	—
131	#13083574	—	2	4	no	—
132	#13083573	—	2	4	no	—
133	#13083573	—	2	8	no	—
134	#13083573	—	2	8	no	—
135	#13083573	—	2	8	no	—
136	#13083573	D₄	1	8	yes	complemented
137	C₂×Dic₁₇₈	—	2	8	no	—
138	C₂×Dic₁₇₈	—	2	4	no	—
139	C₂×Dic₁₇₈	C₂³	1	2	yes	—
140	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
141	C₂×Dic₁₇₈	C₂³	1	2	yes	—
142	C₂×Dic₁₇₈	C₂³	1	2	yes	—
143	C₂×Dic₁₇₈	C₂³	1	2	yes	—
144	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
146	Q₈×D₈₉	—	2	4	no	—
147	Q₈×D₈₉	—	2	4	no	—
148	Q₈×D₈₉	—	2	4	no	—
149	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
150	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
151	C₂×D₃₅₆	C₂³	1	2	yes	—
152	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
153	C₂×D₃₅₆	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
163	D₄×D₈₉	—	2	4	no	—
164	D₄×D₈₉	—	2	8	no	—
165	C₂²×Dic₈₉	C₂³	1	2	yes	—
166	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
167	C₂²×Dic₈₉	C₂³	1	2	yes	—
168	C₂²×Dic₈₉	C₂³	1	2	yes	—
169	C₂²×Dic₈₉	C₂³	1	2	yes	—
170	C₂×C₄×D₈₉	—	2	8	no	—
171	C₂×C₄×D₈₉	—	2	4	no	—
172	C₂×C₄×D₈₉	C₂³	1	2	yes	—
173	C₂×C₄×D₈₉	C₂³	1	2	yes	—
174	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄×D₈₉	C₂³	1	2	yes	—
177	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₈₉	C₂³	1	2	yes	—
179	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₈₉	C₂³	1	2	yes	—
181	C₂×C₄×D₈₉	C₂³	1	2	yes	—
182	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
183	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₈₉	C₂³	1	2	yes	—
186	#13083553	C₂³	1	1	yes	characteristic
187	#13083553	C₂³	1	2	yes	—
188	#13083553	C₂³	1	1	yes	characteristic
189	#13083553	C₂³	1	2	yes	—
190	#13083553	C₂³	1	2	yes	—
191	#13083553	C₂³	1	2	yes	—
192	#13083553	C₂³	1	1	yes	characteristic
193	#13083553	C₂³	1	2	yes	—
194	#13083553	C₂³	1	1	yes	characteristic
195	#13083553	C₂³	1	2	yes	—
196	#13083553	C₂³	1	2	yes	—
197	#13083553	C₂³	1	2	yes	—
198	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
199	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
200	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
202	#13083551	C₂³	1	1	yes	characteristic
203	#13083551	C₂³	1	1	yes	characteristic
204	#13083551	C₂³	1	2	yes	—
205	#13083551	C₂³	1	2	yes	—
206	#13083551	C₂³	1	1	yes	characteristic
207	#13083551	C₂³	1	1	yes	characteristic
208	#13083551	C₂³	1	2	yes	—
209	#13083551	C₂³	1	2	yes	—
210	#13083551	C₂³	1	2	yes	—
211	#13083551	C₂³	1	1	yes	characteristic
212	#13083551	C₂³	1	1	yes	characteristic
213	#13083551	C₂³	1	2	yes	—
214	#13083551	C₂³	1	2	yes	—
215	#13083551	C₂³	1	2	yes	—
216	#13083551	C₂³	1	2	yes	—
217	C₄×Dic₈₉	C₂³	1	2	yes	—
218	C₄×Dic₈₉	C₂³	1	2	yes	—
219	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
220	#41×C₈₉	—	2	4	no	—
221	#41×C₈₉	—	2	4	no	—
222	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
224	C₂×D₄×C₈₉	C₂³	1	2	yes	—
225	C₂×D₄×C₈₉	C₂³	1	2	yes	—
226	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
233	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
234	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
235	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
237	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
239	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
240	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
241	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
242	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
243	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
244	C₄²×C₈₉	C₂³	1	1	yes	characteristic
245	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂³×C₈₉	C₂⁴	1	2	yes	—
248	C₂²×D₈₉	—	2	4	no	—
249	C₂²×D₈₉	—	2	2	no	—
250	C₂²×D₈₉	—	2	2	no	—
251	C₂²×D₈₉	—	2	4	no	—
252	C₂²×D₈₉	—	4	1	no	—
253	C₂²×D₈₉	—	4	2	no	—
254	C₂²×D₈₉	C₂⁴	1	2	yes	—
255	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
257	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
258	Q₈×C₈₉	—	2	2	no	—
259	Q₈×C₈₉	—	2	2	no	—
260	D₄×C₈₉	—	2	4	no	—
261	D₄×C₈₉	—	2	4	no	—
262	D₄×C₈₉	—	4	1	no	—
263	D₄×C₈₉	C₂×D₄	1	4	yes	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	4	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	2	2	no	—
268	C₂×C₄×C₈₉	—	4	2	no	—
269	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
272	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²⋊D₈₉	—	2	4	no	—
278	C₂²⋊D₈₉	—	2	4	no	—
279	C₂²⋊D₈₉	—	2	2	no	—
280	C₂²⋊D₈₉	—	2	2	no	—
281	C₂²⋊D₈₉	—	2	4	no	—
282	C₂²⋊D₈₉	—	2	2	no	—
283	C₂²⋊D₈₉	—	4	2	no	—
284	C₂²⋊D₈₉	—	4	1	no	—
285	C₂²⋊D₈₉	C₂×D₄	1	8	yes	—
286	C₂×Dic₈₉	—	2	4	no	—
287	C₂×Dic₈₉	—	2	2	no	—
288	C₂×Dic₈₉	—	2	4	no	—
289	C₂×Dic₈₉	—	4	2	no	—
290	C₂×Dic₈₉	C₂×D₄	1	8	yes	—
291	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₈₉	C₂⁴	1	2	yes	—
294	C₂×Dic₈₉	C₂⁴	1	2	yes	—
295	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₈₉	C₂⁴	1	2	yes	—
298	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
299	D₃₅₆	—	2	4	no	—
300	D₃₅₆	—	2	2	no	—
301	D₃₅₆	—	2	2	no	—
302	D₃₅₆	—	2	2	no	—
303	D₃₅₆	—	4	2	no	—
304	C₄×D₈₉	—	2	2	no	—
305	C₄×D₈₉	—	2	4	no	—
306	C₄×D₈₉	—	2	2	no	—
307	C₄×D₈₉	—	2	2	no	—
308	C₄×D₈₉	—	2	2	no	—
309	C₄×D₈₉	—	2	4	no	—
310	C₄×D₈₉	—	2	4	no	—
311	C₄×D₈₉	—	2	4	no	—
312	C₄×D₈₉	—	2	4	no	—
313	C₄×D₈₉	—	4	2	no	—
314	C₄×D₈₉	C₂×D₄	1	4	yes	—
315	Dic₁₇₈	—	2	2	no	—
316	Dic₁₇₈	—	2	4	no	—
317	Dic₁₇₈	—	2	4	no	—
318	Dic₁₇₈	—	2	4	no	—
319	Dic₁₇₈	—	2	4	no	—
320	Dic₁₇₈	—	2	2	no	—
321	Dic₁₇₈	C₂×D₄	1	4	yes	—
322	C₂²×C₈₉	—	2	2	no	—
323	C₂²×C₈₉	—	2	2	no	—
324	C₂²×C₈₉	—	2	1	no	—
325	C₂²×C₈₉	—	2	1	no	—
326	C₂²×C₈₉	—	2	1	no	—
327	C₂²×C₈₉	—	2	1	no	—
328	C₂²×C₈₉	—	2	1	no	—
329	C₂²×C₈₉	—	2	1	no	—
330	C₂²×C₈₉	C₂²×D₄	1	4	yes	—
331	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
332	C₂×D₈₉	—	2	1	no	—
333	C₂×D₈₉	—	2	1	no	—
334	C₂×D₈₉	—	2	1	no	—
335	C₂×D₈₉	—	2	1	no	—
336	C₂×D₈₉	—	2	1	no	—
337	C₂×D₈₉	—	2	2	no	—
338	C₂×D₈₉	—	2	1	no	—
339	C₂×D₈₉	—	2	2	no	—
340	C₂×D₈₉	—	2	1	no	—
341	C₂×D₈₉	—	2	2	no	—
342	C₂×D₈₉	—	4	4	no	—
343	C₂×D₈₉	—	4	8	no	—
344	C₂×D₈₉	C₂²×D₄	1	2	yes	—
345	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	complemented
346	C₄×C₈₉	—	2	1	no	—
347	C₄×C₈₉	—	2	2	no	—
348	C₄×C₈₉	—	2	2	no	—
349	C₄×C₈₉	—	2	1	no	—
350	C₄×C₈₉	—	2	1	no	—
351	C₄×C₈₉	—	2	2	no	—
352	C₄×C₈₉	—	2	1	no	—
353	C₄×C₈₉	C₂²×D₄	1	2	yes	—
354	Dic₈₉	—	2	2	no	—
355	Dic₈₉	—	2	1	no	—
356	Dic₈₉	—	2	1	no	—
357	Dic₈₉	—	2	1	no	—
358	Dic₈₉	—	2	2	no	—
359	Dic₈₉	—	2	1	no	—
360	Dic₈₉	C₂²×D₄	1	4	yes	—
361	Dic₈₉	C₂²×D₄	1	2	yes	—
362	C₂×C₈₉	—	2	4	no	—
363	C₂×C₈₉	—	4	1	no	—
364	C₂×C₈₉	—	4	1	no	—
365	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
366	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂×C₈₉	#585	1	1	yes	characteristic
368	D₈₉	—	2	2	no	—
369	D₈₉	—	2	2	no	—
370	D₈₉	—	4	1	no	—
371	D₈₉	—	4	2	no	—
372	#3489	—	89	1	no	maximal, Sylow
373	C₈₉	#3489	1	1	yes	characteristic, complemented, Sylow
374	C₂×2₋¹⁺⁴	—	89	1	no	—
375	C₂²×#41	—	89	1	no	—
376	D₄×Q₈	—	89	1	no	—
377	D₄×Q₈	—	89	1	no	—
378	#548	—	89	1	no	—
379	#548	—	89	1	no	—
380	#547	—	89	1	no	—
381	#547	—	89	2	no	—
382	#547	—	89	2	no	—
383	#547	D₈₉	1	1	yes	characteristic, complemented
384	#546	—	89	1	no	—
385	#546	—	89	2	no	—
386	#546	—	89	2	no	—
387	#546	—	89	1	no	—
388	#537	—	89	1	no	—
389	#537	—	89	2	no	—
390	#536	—	89	1	no	—
391	#536	—	89	2	no	—
392	#525	—	89	2	no	—
393	#525	—	89	1	no	—
394	C₂×C₂²⋊Q₈	—	89	1	no	—
395	C₂×C₂²⋊Q₈	—	89	2	no	—
396	#520	—	89	1	no	—
397	2₋¹⁺⁴	—	178	8	no	—
398	C₂×#41	—	89	1	no	—
399	C₂×#41	—	89	1	no	—
400	C₂×#41	—	89	2	no	—
401	C₂×#41	—	89	2	no	—
402	C₂×#41	—	89	1	no	—
403	C₂×#41	—	89	2	no	—
404	C₂×#41	—	89	1	no	—
405	C₂×#41	—	89	2	no	—
406	C₂×#41	—	89	2	no	—
407	C₂×#41	—	89	1	no	—
408	C₂×#41	—	178	8	no	—
409	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
410	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
411	C₂²×Q₈	—	89	1	no	—
412	C₂²×Q₈	—	89	1	no	—
413	C₂²×Q₈	—	89	1	no	—
414	C₂²×Q₈	—	89	2	no	—
415	C₂²×Q₈	—	89	1	no	—
416	C₂²×D₄	—	89	2	no	—
417	C₂²×D₄	—	89	1	no	—
418	C₂³×C₄	—	89	2	no	—
419	C₂³×C₄	—	89	1	no	—
420	C₄⋊Q₈	—	89	1	no	—
421	C₄⋊Q₈	—	89	2	no	—
422	C₄⋊Q₈	—	89	2	no	—
423	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
424	#124	—	89	1	no	—
425	#124	—	89	2	no	—
426	#124	—	89	2	no	—
427	#124	—	89	1	no	—
428	#123	—	89	2	no	—
429	#123	—	89	2	no	—
430	#123	—	89	2	no	—
431	#123	—	89	1	no	—
432	#123	—	89	2	no	—
433	#123	—	89	2	no	—
434	#123	—	89	1	no	—
435	#123	—	89	2	no	—
436	#123	C₂×D₈₉	1	2	yes	complemented
437	#123	C₂×D₈₉	1	2	yes	complemented
438	C₂²⋊Q₈	—	89	1	no	—
439	C₂²⋊Q₈	—	89	1	no	—
440	C₂²⋊Q₈	—	89	1	no	—
441	C₂²⋊Q₈	—	89	2	no	—
442	C₂²⋊Q₈	—	89	1	no	—
443	C₂²⋊Q₈	—	89	2	no	—
444	C₂²⋊Q₈	—	89	2	no	—
445	C₂²⋊Q₈	—	89	2	no	—
446	C₂²⋊Q₈	—	89	2	no	—
447	C₂²⋊Q₈	—	89	2	no	—
448	C₂²⋊Q₈	—	89	2	no	—
449	C₂²⋊Q₈	—	89	1	no	—
450	C₂²⋊Q₈	—	89	2	no	—
451	C₂²⋊Q₈	—	89	2	no	—
452	C₂²⋊Q₈	—	89	2	no	—
453	C₂²⋊Q₈	—	89	1	no	—
454	C₂²⋊Q₈	—	89	2	no	—
455	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
456	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
457	#121	—	89	1	no	—
458	#121	—	89	2	no	—
459	#121	—	89	2	no	—
460	#121	—	89	2	no	—
461	#121	—	89	2	no	—
462	#121	—	89	1	no	—
463	#121	—	89	2	no	—
464	#121	—	89	1	no	—
465	#121	—	89	1	no	—
466	#121	—	89	2	no	—
467	#121	—	89	2	no	—
468	#121	—	89	2	no	—
469	#121	C₂×D₈₉	1	2	yes	complemented
470	#120	—	89	2	no	—
471	#120	—	89	1	no	—
472	#120	—	89	1	no	—
473	#120	—	89	2	no	—
474	C₄×Q₈	—	89	1	no	—
475	C₄×Q₈	—	89	1	no	—
476	C₄×D₄	—	89	1	no	—
477	C₄×D₄	—	89	1	no	—
478	C₄×D₄	—	89	2	no	—
479	C₄×D₄	—	89	1	no	—
480	C₄×D₄	—	89	2	no	—
481	C₄×D₄	—	89	2	no	—
482	C₄×D₄	—	89	2	no	—
483	C₄×D₄	—	89	2	no	—
484	C₄×D₄	—	89	2	no	—
485	C₄×D₄	—	89	1	no	—
486	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
487	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
488	#117	—	89	2	no	—
489	#117	—	89	1	no	—
490	C₂×C₄⋊C₄	—	89	2	no	—
491	C₂×C₄⋊C₄	—	89	2	no	—
492	C₂×C₄⋊C₄	—	89	1	no	—
493	C₂×C₄⋊C₄	—	89	2	no	—
494	C₂×C₄⋊C₄	C₂×D₈₉	1	2	yes	complemented
495	C₂×C₂²⋊C₄	—	89	2	no	—
496	C₂×C₂²⋊C₄	—	89	2	no	—
497	C₂×C₂²⋊C₄	—	89	2	no	—
498	C₂⁴	—	89	1	no	—
499	C₂⁴	—	89	2	no	—
500	#41	—	2	4	no	—
501	#41	—	2	4	no	—
502	#41	—	89	8	no	—
503	#41	—	178	4	no	—
504	#41	—	178	8	no	—
505	#41	—	178	8	no	—
506	#41	—	178	4	no	—
507	#41	—	178	8	no	—
508	#41	—	178	8	no	—
509	#41	—	178	4	no	—
510	#41	—	178	8	no	—
511	#41	—	178	4	no	—
512	C₂×Q₈	—	89	1	no	—
513	C₂×Q₈	—	89	2	no	—
514	C₂×Q₈	—	89	1	no	—
515	C₂×Q₈	—	89	2	no	—
516	C₂×Q₈	—	89	2	no	—
517	C₂×Q₈	—	89	1	no	—
518	C₂×Q₈	—	89	2	no	—
519	C₂×Q₈	—	178	8	no	—
520	C₂×Q₈	—	178	4	no	—
521	C₂×Q₈	—	178	4	no	—
522	C₂×Q₈	—	178	4	no	—
523	C₂×Q₈	—	178	4	no	—
524	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
525	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
526	C₂×D₄	—	89	2	no	—
527	C₂×D₄	—	89	2	no	—
528	C₂×D₄	—	89	1	no	—
529	C₂×D₄	—	89	1	no	—
530	C₂×D₄	—	89	1	no	—
531	C₂×D₄	—	89	2	no	—
532	C₂×D₄	—	89	1	no	—
533	C₂×D₄	—	89	2	no	—
534	C₂×D₄	—	89	2	no	—
535	C₂×D₄	—	89	2	no	—
536	C₂×D₄	—	89	1	no	—
537	C₂×D₄	—	89	1	no	—
538	C₂×D₄	—	89	2	no	—
539	C₂×D₄	—	89	1	no	—
540	C₂×D₄	—	178	8	no	—
541	C₂×D₄	—	178	4	no	—
542	C₂×D₄	C₂²×D₈₉	1	2	yes	—
543	C₂×D₄	C₂²×D₈₉	1	2	yes	—
544	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
545	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
546	C₂²×C₄	—	89	2	no	—
547	C₂²×C₄	—	89	1	no	—
548	C₂²×C₄	—	89	2	no	—
549	C₂²×C₄	—	89	2	no	—
550	C₂²×C₄	—	89	2	no	—
551	C₂²×C₄	—	89	1	no	—
552	C₂²×C₄	—	89	2	no	—
553	C₂²×C₄	—	89	2	no	—
554	C₂²×C₄	—	89	1	no	—
555	C₂²×C₄	—	89	2	no	—
556	C₂²×C₄	—	89	1	no	—
557	C₂²×C₄	—	89	2	no	—
558	C₂²×C₄	—	89	1	no	—
559	C₂²×C₄	—	89	2	no	—
560	C₂²×C₄	—	89	1	no	—
561	C₂²×C₄	—	89	2	no	—
562	C₂²×C₄	—	178	8	no	—
563	C₂²×C₄	—	178	4	no	—
564	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
565	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
566	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
567	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
568	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
569	C₄⋊C₄	—	89	2	no	—
570	C₄⋊C₄	—	89	1	no	—
571	C₄⋊C₄	—	89	1	no	—
572	C₄⋊C₄	—	89	2	no	—
573	C₄⋊C₄	—	89	2	no	—
574	C₄⋊C₄	—	89	2	no	—
575	C₄⋊C₄	—	89	1	no	—
576	C₄⋊C₄	—	89	2	no	—
577	C₄⋊C₄	—	89	2	no	—
578	C₄⋊C₄	—	89	2	no	—
579	C₄⋊C₄	—	89	2	no	—
580	C₄⋊C₄	—	89	1	no	—
581	C₄⋊C₄	—	89	2	no	—
582	C₄⋊C₄	—	89	1	no	—
583	C₄⋊C₄	—	89	1	no	—
584	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
585	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
586	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
587	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
588	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
589	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
590	C₂²⋊C₄	—	89	2	no	—
591	C₂²⋊C₄	—	89	2	no	—
592	C₂²⋊C₄	—	89	1	no	—
593	C₂²⋊C₄	—	89	1	no	—
594	C₂²⋊C₄	—	89	2	no	—
595	C₂²⋊C₄	—	89	1	no	—
596	C₂²⋊C₄	—	89	2	no	—
597	C₂²⋊C₄	—	89	1	no	—
598	C₂²⋊C₄	—	89	2	no	—
599	C₂²⋊C₄	—	89	2	no	—
600	C₂²⋊C₄	—	89	2	no	—
601	C₂²⋊C₄	—	89	2	no	—
602	C₂²⋊C₄	—	89	1	no	—
603	C₂²⋊C₄	—	89	1	no	—
604	C₂²⋊C₄	—	89	1	no	—
605	C₂²⋊C₄	—	89	2	no	—
606	C₂²⋊C₄	—	89	2	no	—
607	C₂²⋊C₄	—	89	2	no	—
608	C₂²⋊C₄	—	89	1	no	—
609	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
610	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
611	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
612	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
613	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
614	C₄²	—	89	2	no	—
615	C₄²	—	89	2	no	—
616	C₄²	—	89	1	no	—
617	C₄²	C₂²×D₈₉	1	1	yes	characteristic
618	C₂³	—	89	1	no	—
619	C₂³	—	89	1	no	—
620	C₂³	—	89	2	no	—
621	C₂³	—	89	1	no	—
622	C₂³	—	356	2	no	—
623	C₂³	—	356	1	no	—
624	C₂³	—	178	2	no	—
625	C₂³	—	178	4	no	—
626	C₂³	—	178	2	no	—
627	C₂³	—	178	4	no	—
628	C₂³	C₂³×D₈₉	1	1	yes	characteristic
629	C₂³	C₂³×D₈₉	1	1	yes	characteristic
630	C₂³	C₂³×D₈₉	1	2	yes	—
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	89	4	no	—
634	Q₈	—	178	2	no	—
635	Q₈	—	178	4	no	—
636	Q₈	—	178	4	no	—
637	Q₈	—	178	4	no	—
638	Q₈	—	178	4	no	—
639	Q₈	—	178	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	1	no	—
643	D₄	—	89	8	no	—
644	D₄	—	356	2	no	—
645	D₄	—	356	2	no	—
646	D₄	—	356	1	no	—
647	D₄	—	178	2	no	—
648	D₄	—	178	4	no	—
649	D₄	—	178	2	no	—
650	D₄	—	178	4	no	—
651	D₄	—	178	2	no	—
652	D₄	—	178	2	no	—
653	D₄	—	178	2	no	—
654	D₄	—	178	4	no	—
655	D₄	—	178	4	no	—
656	D₄	—	178	2	no	—
657	D₄	D₄×D₈₉	1	4	yes	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	89	8	no	—
664	C₂×C₄	—	89	2	no	—
665	C₂×C₄	—	89	1	no	—
666	C₂×C₄	—	89	4	no	—
667	C₂×C₄	—	89	1	no	—
668	C₂×C₄	—	89	1	no	—
669	C₂×C₄	—	89	2	no	—
670	C₂×C₄	—	89	2	no	—
671	C₂×C₄	—	89	1	no	—
672	C₂×C₄	—	89	1	no	—
673	C₂×C₄	—	356	2	no	—
674	C₂×C₄	—	356	2	no	—
675	C₂×C₄	—	178	2	no	—
676	C₂×C₄	—	178	4	no	—
677	C₂×C₄	—	178	4	no	—
678	C₂×C₄	—	178	4	no	—
679	C₂×C₄	—	178	4	no	—
680	C₂×C₄	—	178	2	no	—
681	C₂×C₄	—	178	4	no	—
682	C₂×C₄	—	178	2	no	—
683	C₂×C₄	—	178	4	no	—
684	C₂×C₄	—	178	4	no	—
685	C₂×C₄	—	178	2	no	—
686	C₂×C₄	—	178	2	no	—
687	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
688	C₂×C₄	C₂³×D₈₉	1	2	yes	—
689	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
690	C₂×C₄	C₂³×D₈₉	1	2	yes	—
691	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
692	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
693	C₂×C₄	C₂³×D₈₉	1	2	yes	—
694	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	89	2	no	—
704	C₂²	—	89	2	no	—
705	C₂²	—	356	8	no	—
706	C₂²	—	356	4	no	—
707	C₂²	—	178	1	no	—
708	C₂²	—	178	2	no	—
709	C₂²	—	178	1	no	—
710	C₂²	—	178	2	no	—
711	C₂²	—	178	1	no	—
712	C₂²	—	178	2	no	—
713	C₂²	—	178	1	no	—
714	C₂²	—	178	1	no	—
715	C₂²	—	178	1	no	—
716	C₂²	—	178	1	no	—
717	C₂²	C₂×D₄×D₈₉	1	4	yes	—
718	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	2	no	—
726	C₄	—	89	2	no	—
727	C₄	—	89	4	no	—
728	C₄	—	178	1	no	—
729	C₄	—	178	2	no	—
730	C₄	—	178	1	no	—
731	C₄	—	178	1	no	—
732	C₄	—	178	2	no	—
733	C₄	—	178	1	no	—
734	C₄	C₂×D₄×D₈₉	1	2	yes	—
735	C₂	—	2	4	no	—
736	C₂	—	4	1	no	—
737	C₂	—	4	1	no	—
738	C₂	—	356	2	no	—
739	C₂	—	356	1	no	—
740	C₂	—	178	2	no	—
741	C₂	—	178	2	no	—
742	C₂	C₂²×D₄×D₈₉	1	1	yes	characteristic
743	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
744	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#547×C₈₉	C₂
hypercenter	#547	D₈₉
hypocenter	C₈₉	#3489
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#15668059	C₂	semidirect
2. C₂×#41×D₈₉	C₂	semidirect
3. #19152263	C₂	semidirect
4. #19152261	C₂	semidirect
5. #19152258	C₂	semidirect
6. #19152257	C₂	semidirect
7. #19152249	C₂	semidirect
8. #19152247	C₂	semidirect
9. #19152246	C₂	semidirect
10. #19152243	C₂	semidirect
11. #19152240	C₂	semidirect
12. #19152237	C₂	semidirect
13. #19152236	C₂	semidirect
14. #19152178	C₂	semidirect
15. #19152175	C₂	semidirect
16. #19152173	C₂	semidirect
17. #19152170	C₂	semidirect
18. #19152107	C₂	semidirect
19. #19152106	C₂	semidirect
20. C₂×#15667990	C₂	semidirect
21. C₂²⋊Q₈×D₈₉	C₂	semidirect
22. #19152077	C₂	semidirect
23. #547×C₈₉	C₂	semidirect
28. C₂×#13083574	C₂²	semidirect
29. C₂×#13083574	C₂²	semidirect
32. C₂×#13083573	C₂²	semidirect
33. C₂×#13083573	C₂²	semidirect
34. C₂×#13083573	C₂²	semidirect
36. C₂²×Dic₁₇₈	C₂²	semidirect
37. C₂²×Dic₁₇₈	C₂²	semidirect
39. C₂×Q₈×D₈₉	C₂²	semidirect
40. C₂×Q₈×D₈₉	C₂²	semidirect
45. #15668011	C₂²	semidirect
46. #15668011	C₂²	semidirect
47. #15668010	C₂²	semidirect
48. #15668001	C₂²	semidirect
49. #15668000	C₂²	semidirect
50. #15667998	C₂²	semidirect
51. #15667998	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667997	C₂²	semidirect
54. #15667997	C₂²	semidirect
55. #15667996	C₂²	semidirect
56. #15667995	C₂²	semidirect
57. #15667995	C₂²	semidirect
58. #15667994	C₂²	semidirect
59. #15667993	C₂²	semidirect
61. #15667991	C₂²	semidirect
66. #15667990	C₂²	semidirect
67. #15667990	C₂²	semidirect
68. #15667990	C₂²	semidirect
69. #15667990	C₂²	semidirect
70. #15667990	C₂²	semidirect
71. #15667990	C₂²	semidirect
72. #15667989	C₂²	semidirect
73. #15667989	C₂²	semidirect
74. #15667989	C₂²	semidirect
76. #15667988	C₂²	semidirect
77. #15667987	C₂²	semidirect
78. #15667987	C₂²	semidirect
79. #15667986	C₂²	semidirect
80. #15667986	C₂²	semidirect
82. #15667985	C₂²	semidirect
83. #15667985	C₂²	semidirect
84. #15667985	C₂²	semidirect
85. #15667984	C₂²	semidirect
86. #15667984	C₂²	semidirect
87. #15667984	C₂²	semidirect
88. #15667984	C₂²	semidirect
93. C₄×Dic₁₇₈	C₂²	semidirect
94. #15667977	C₂²	semidirect
96. D₄×Dic₈₉	C₂²	semidirect
98. #15667974	C₂²	semidirect
100. C₄×C₂²⋊D₈₉	C₂²	semidirect
101. C₄×C₂²⋊D₈₉	C₂²	semidirect
103. #15667972	C₂²	semidirect
104. #15667972	C₂²	semidirect
105. #15667969	C₂²	semidirect
106. #15667968	C₂²	semidirect
107. C₂×#13083553	C₂²	semidirect
108. C₂×#13083553	C₂²	semidirect
109. C₄⋊C₄×D₈₉	C₂²	semidirect
110. C₄⋊C₄×D₈₉	C₂²	semidirect
115. C₂×#41×C₈₉	C₂²	semidirect
116. C₄⋊Q₈×C₈₉	C₂²	semidirect
117. #123×C₈₉	C₂²	semidirect
118. #123×C₈₉	C₂²	semidirect
119. C₂²⋊Q₈×C₈₉	C₂²	semidirect
120. C₂²⋊Q₈×C₈₉	C₂²	semidirect
121. #121×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
123. C₄×D₄×C₈₉	C₂²	semidirect
124. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
136. #13083573	D₄	semidirect
345. C₂×D₈₉	2₋¹⁺⁴	semidirect
373. C₈₉	#3489	semidirect
383. #547	D₈₉	semidirect
410. C₂×#41	C₂×D₈₉	semidirect
423. C₄⋊Q₈	C₂×D₈₉	semidirect
436. #123	C₂×D₈₉	semidirect
437. #123	C₂×D₈₉	semidirect
455. C₂²⋊Q₈	C₂×D₈₉	semidirect
456. C₂²⋊Q₈	C₂×D₈₉	semidirect
469. #121	C₂×D₈₉	semidirect
486. C₄×D₄	C₂×D₈₉	semidirect
487. C₄×D₄	C₂×D₈₉	semidirect
494. C₂×C₄⋊C₄	C₂×D₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15668059	2
C₂×#41×D₈₉	2
#19152263	2
#19152261	2
#19152258	2
#19152257	2
#19152249	2
#19152247	2
#19152246	2
#19152243	2
#19152240	2
#19152237	2
#19152236	2
#19152178	2
#19152175	2
#19152173	2
#19152170	2
#19152107	2
#19152106	2
C₂×#15667990	2
C₂²⋊Q₈×D₈₉	2
#19152077	2
#547×C₈₉	2
#3489	89